This review paper discusses recent efforts to passively move unwanted energy from a primary structure to a local essentially non-linear attachment (termed a non-linear energy sink) by utilizing targeted energy transfer (TET) (or non-linear energy pumping). First, fundamental theoretical aspects of TET will be discussed, including the essentially non-linear governing dynamical mechanisms for TET. Then, results of experimental studies that validate the TET phenomenon will be presented. Finally, some current engineering applications of TET will be discussed. The concept of TET may be regarded as contrary to current common engineering practise, which generally views non-linearities in engineering systems as either unwanted or, at most, as small perturbations of linear behaviour. Essentially non-linear stiffness elements are intentionally introduced in the design that give rise to new dynamical phenomena that are very beneficial to the design objectives and have no counterparts in linear theory. Care, of course, is taken to avoid some of the unwanted dynamic effects that such elements may introduce, such as chaotic responses or other responses that are contrary to the design objectives. [less ▲]